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	<h1>Weibull regression in censored survival analysis; <br>
	A comparison with BUGS</h1>
		<br><br>
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             <font face="Arial, Helvetica" color="White"><b>ADMB Files</b></font>
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			     <td>
                     Code: <a href="kidney.tpl">kidney.tpl</a><br>
                     Data: 		<a href="kidney.dat">kidney.dat</a><br>
                     Initial values: <a href="kidney.pin">kidney.pin</a><br>
<!--
                     All required files (DOS): <a href="kidney.zip">kidney.zip</a><br>
					 All required files (linux): <a href="kidney.tar.gz">kidney.tar.gz</a><br>					 
-->
                     Expected Results: <a href="kidney-expected-results.par">kidney.par</a><br>
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			     <td>
                     In a <a href="../admb_tutorial.html">DOS</a> window<br> 
					 Under <a href="../admb_tutorial.html">linux</a><br>
				   </font>
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             <font face="Arial, Helvetica" color="White"><b>Results: Computation times</b></font>
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			     <td>
                     ADMB-RE: 9 seconds.<br>
					BUGS: 7 seconds,<br>
					which was the time taken by WinBUGS 1.4 to perform 
					1,000 iterations of two parallel chains.
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 <td width="75%">
<h3><strong>Model description</strong></h3>

The collection of examples following <a HREF="http://www.mrc-bsu.cam.ac.uk/bugs/">WinBUGS</a> (Volume 1, WinBUGS 1.4) 
contains an application of Cox's proportional hazard model with random effects. A Weibull baseline hazard is used: <br>
<br>
<div align="center"><em>h<sub>0</sub>(t)</em> = <em>r*t<sup>r-1</sup></em>,  <em>r>0.</em></div>
<br>
The "kidney data" contain information on time-to-infection for 38 patients, and there are several explanatory variables (see table below).
A full description of the model can be found here: <a href="kidney.pdf">kidney.pdf</a>. 


 
<h3><strong>Comparison with BUGS</strong></h3>
Parameter estimates for the kidney data are shown in the following table.<br>

<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="LEFT"></TD>
<TD ALIGN="LEFT"><FONT FACE="Symbol">b</FONT><sub><em>0</em></sub></TD>
<TD ALIGN="LEFT"><FONT FACE="Symbol">b</FONT><sub>age</sub></TD>
<TD ALIGN="LEFT"><FONT FACE="Symbol">b</FONT><sub><em>1</em></sub></TD>
<TD ALIGN="LEFT"><FONT FACE="Symbol">b</FONT><sub><em>2</em></sub></TD>
<TD ALIGN="LEFT"><FONT FACE="Symbol">b</FONT><sub><em>3</em></sub></TD>
<TD ALIGN="LEFT"><FONT FACE="Symbol">b</FONT><sub>sex</sub></TD>
<TD ALIGN="LEFT">r</TD>
<TD ALIGN="LEFT"><FONT FACE="Symbol">s</FONT></TD>
</TR>

<TR><TD ALIGN="LEFT">ADMB-RE</TD>
<TD ALIGN="LEFT">-4.344</TD>
<TD ALIGN="LEFT">0.003</TD>
<TD ALIGN="LEFT">0.1208</TD>
<TD ALIGN="LEFT">0.6058</TD>
<TD ALIGN="LEFT">-1.1423</TD>
<TD ALIGN="LEFT">-1.8767</TD>
<TD ALIGN="LEFT">1.1624</TD>
<TD ALIGN="LEFT">0.5617</TD>
</TR>
<TR><TD ALIGN="LEFT">Std. dev.</TD>
<TD ALIGN="LEFT">0.872</TD>
<TD ALIGN="LEFT">0.0137</TD>
<TD ALIGN="LEFT">0.5008</TD>
<TD ALIGN="LEFT">0.5011</TD>
<TD ALIGN="LEFT">0.7729</TD>
<TD ALIGN="LEFT">0.4754</TD>
<TD ALIGN="LEFT">0.1626</TD>
<TD ALIGN="LEFT">0.297</TD>
</TR>
<TR><TD ALIGN="LEFT"><a HREF="http://www.mrc-bsu.cam.ac.uk/bugs/">WinBUGS</a></TD>
<TD ALIGN="LEFT">-4.6</TD>
<TD ALIGN="LEFT">0.003</TD>
<TD ALIGN="LEFT">0.1329</TD>
<TD ALIGN="LEFT">0.6444</TD>
<TD ALIGN="LEFT">-1.168</TD>
<TD ALIGN="LEFT">-1.938</TD>
<TD ALIGN="LEFT">1.215</TD>
<TD ALIGN="LEFT">0.6374</TD>
</TR>
<TR><TD ALIGN="LEFT">Std. dev.</TD>
<TD ALIGN="LEFT">0.8962</TD>
<TD ALIGN="LEFT">0.0148</TD>
<TD ALIGN="LEFT">0.5393</TD>
<TD ALIGN="LEFT">0.5301</TD>
<TD ALIGN="LEFT">0.8335</TD>
<TD ALIGN="LEFT">0.4854</TD>
<TD ALIGN="LEFT">0.1623</TD>
<TD ALIGN="LEFT">0.357</TD>
</TR>
</TABLE>
</DIV>



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